Distortion-minimized de-homogenization for optimization of cell-size distribution in TPMS structures

This paper presents a homogenized topology optimization (TO) method for spatially optimizing cell-size distribution of triply-periodic minimal surface (TPMS) structures, with high accuracy in the optimized structural response after de-homogenization. To achieve this, we introduce a novel de-homogenization technique that directly minimizes the difference between the wavenumbers obtained from the target and actual size distributions. This minimization problem is efficiently solved as a typical Poisson’s equation utilizing the discrete cosine transform (DCT). We first verify the proposed de-homogenization method through numerical examples, showcasing its capability in significantly reducing the known distortion of the de-homogenized TPMS structures from the conventional periodic modulation (PM) method. Then, we apply the proposed method to a stiffness maximization problem, to demonstrate its effectiveness in improving the structural response compared to the PM method, through numerical examples and experimental validation. The proposed method successfully reduced the distortion of the de-homogenized structures compared to the PM method, leading to 0.8% difference in the strain energy compared to the homogenized model, as opposed to 63.6% difference in the PM method. The optimized structure from the proposed method shows a significant improvement in the strain energy by 50.1% compared to the uniform case in the FE analysis on the de-homogenized models, while the PM method results in a significant decrease of 45.8%. The experimental validation shows that the effective stiffness of the optimized structure from the proposed method is 54.2% higher than that of the uniform case, while the PM method results in a significant decrease by 77.3%. These results exhibit the proposed method effectively increases the accuracy of the de-homogenization, thereby maximizing the potential of the homogenized TO for the spatial cell-size optimization of TPMS structures.